In the art of measuring mass flow rates for flowing substances it is known that flowing a fluid through a rotating or oscillating conduit produces Coriolis forces which are perpendicular to both the velocity of the mass moving through the conduit and the angular velocity vector of the rotation or oscillation of the conduit. It is also known that the magnitude of such Coriolis forces is related to the mass flow rate as a function of the angular velocity of the conduit.
One of the major technical problems previously associated with Coriolis mass flow rate instruments was the accurate measurement of Coriolis force effects such as conduit deflection. This problem arises in part because the magnitude of the Coriolis forces for moderate mass flow rates and reasonable angular velocities may be very small, resulting in very small deflection or other effects, which necessitates the use of sensitive and accurate instrumentation. Furthermore, in order to determine the mass flow rate passing through the conduit as a function of the magnitude of the generated Coriolis forces, the magnitude of the angular velocity of the conduit must also be either accurately measured or precisely controlled.
A mechanical configuration and measurement technique which, among other advantages, avoids the need to measure or control the magnitude of the angular velocity of the conduit, and concurrently provides requisite sensitivity and accuracy of measurement of the effects caused by generated Coriolis forces is taught in U.S. Pat. No. 4,187,721. The mechanical configuration disclosed in that patent incorporates a resilient U-shaped flow tube which has no pressure sensitive joints, and is cantilever mounted at the open ends of the U-tube so as to be capable of being elastically oscillated about an axis perpendicular to the side legs of the U-tube, which axis is located near the fixed mounting and in the plane in which the U-tube lies when at rest; i.e., the mid-plane of oscillation. When a substance is flowing through the U-tube, and that tube is thus mounted, oscillation of the filled U-tube so that its free end passes through the mid-plane of oscillation, causes the generation of a Coriolis force couple which elastically deflects the yoke portion of the U-tube about an axis located in the plane of the U-tube midway between and parallel to the side legs of the U-tube. By designing the mounted U-tube so that it has a resonant frequency about the axis perpendicular to the side legs of the U-tube that is lower than the resonant frequency about the axis parallel to the side legs of the U-tube, and by then oscillating the U-tube about the axis perpendicular to the side legs of the U-tube at its resonant frequency, a mechanical situation is created whereby the forces which oppose the generated Coriolis forces are predominantly linear spring forces. The fact that the forces opposing the generated Coriolis forces are predominantly linear spring forces causes one side leg of the U-tube to pass through the mid-plane of oscillation before the other side leg does so, in a linear fashion. Occurrence of these events results in a situation where measurement of the time interval between the passage of the respective side legs through the mid-plane of oscillation provides a direct means, without regard to the angular velocity of the U-tube or other variable terms, for calculating the mass flow rate passing through the U-tube. Such time difference measurements can accurately be made by using optical sensors as disclosed in U.S. Pat. No. 4,187,721, or by using electromagnetic velocity sensors as disclosed in co-pending patent application Ser. No. 280,297 of James E. Smith, filed July 6, 1981 as a continuation-in-part of application Ser. No. 235,268 of James E. Smith filed Feb. 17, 1981, now abandoned.
Since the sensitivity of Coriolis mass flow rate instruments of the type described is primarily dependent on the magnitude of elastic deflection about the axis parallel to the side legs, and because the Coriolis force couple causing such deflections is a weak force couple, increases in sensitivity can directly be accomplished by reducing the magnitude of the opposing spring forces.
The fluid flow meters described in U.S. Pat. No. 4,187,721 and co-pending application Ser. No. 280,297 are capable of measuring mass flow rates of a very wide variety of fluids, including liquids, both Newtonian and non-Newtonian, gases and multi-phase fluids such as gas-liquid or gas-solid combinations. As the mass flow rates of the fluids being measured become very low, however, improving the sensitivity of these instruments becomes increasingly important.
An example of an application where mass flow rates are very low is when the mass flow rate of gases or multi-phase combinations are measured. Examples of multi-phase combinations include solid catalyst particles suspended in a gas, grain such as wheat transported by a gas, liquids suspended above their dew point in a gas, etc. A means for increasing the sensitivity of the flow meter instruments is to decrease the wall thickness of the U-tube, which reduces the spring forces opposing the generated Coriolis forces. The degree of reduction in the wall thickness of the U-tube that is achievable, however, is limited by pressure considerations. Thus, e.g., if the mass flow rates of high pressure gases are to be measured, the wall of the U-tube must be thick enough to contain the gas which, of course, exacerbates efforts to increase instrument sensitivity.